magnetic circular dichroism spectroscopy -...

Magnetic Circular Dichroism Spectroscopy

Frank Neese

Max Planck Institute for Chemical Energy Conversion Stiftstr.34-36

Mülheim an der Ruhr

The Faraday Effect

f : Rotation angle of plane polarized light

V : Verdet Constant

B : Magnetic Field

d : Length of Light Path

Today worked with lines of magnetic force, passing them across different bodies (transparent in different directions) and at the same time passing a polarised ray of light through them.,,, A piece of heavy glass which was 2 inches by 1.8 inches, and an inch thick, being a silico borate of lead, and polished on the two shortest edges was experimented with. It gave no effects when the same magnetic poles or the contrary poles were on opposite sides (as respect the course of the polarised ray) – nor when the same poles were on the same side, either with the constant or intermitting current – BUT when the contrary magnetic poles were on the same side, there was an effect produced on the polarised ray, and thus magnetic force and light were proved to have relation to each other. This fact will most likely prove exceeding fertile and of great value in the investigations of both conditions of natural force (Faraday‘s diary – 13th September 1845. Vol. IV, G. Bell and Sons Ltd., London 1933)

Michael Faraday 1791-1867

The Faraday Effect

Faradays actual horseshoe magnet (1845)

(Faraday Museum, London)

Molecular property (wavelength dependent)

Circular Dichroism vs Optical Rotary Dispersion

ORD : optical rotation of plane polarized light as f(l) (dispersive)

CD : Differential absorption of right and left circularly polarized light as f(l) (absorptive)

Kramers-Kronig Transform

ABSCD

ORD

l

q

e De

Photons, Electrons, States, Spectra & all that

Anatomy of a Light Wave

★ Wavelength: λ ★ Frequency: ω=2πc/λ ★ Electric Field: E ★ Magnetic Field: B ★ Propagation Direction: e ★ Wave vector k (|k|= 2π/λ) ★ Momentum: p=h/2πk ★ Angular Momentum:±h/2π

E

B

λ

★ Linear Polarization

1

2k + + k−( )

★ Circular Polarization (RCP, LCP) k + or k−

k

Energy Scale of Optical Spectroscopy

4 - 1eV 8000 2000 0.1-0.01 10-4 -10-5 10-6 -10-7

X-Ray UV/vis Infrared Microwave RadiowaveGamma

EPR ENDOR

NMR

IR

Raman

ABS

MCD

CD

XAS EXAFS

Möss- bauer

14000

STATES of a SystemO

rbita

l ene

rgy

ONE-ELECTRONIC-STATE of a molecule:

Configuration:Distribution of electrons among orbitals (singly- and doubly occupied orbitals) nI

|nISMG> ≡ ΨISM ;Γ

„wavefunction“ for this STATEa−3 B

1g≡ Ψ

0

11;B1g

Total spin:Coupling of unpaired electrons to a given total spin S and spin-projection M

Symmetry:Direct product of symmetries of singly occupied molecular orbitals G

Excited States in Transition Metal ComplexesO

rbita

l Ene

rgy

} } } }

Ligand1

Ligand2

Metal d-shell

Ligand1

d-d Excitation

LMCT Excitation

MLCT Excitation

Intra Ligand

Excitation

Ligand-to Ligand (LLCT)

Excitation

d-d Excited States of Transition Metals: LFT!

dxy dxz dyz

dx2-y2 dz2

dxy dxz dyz

dx2-y2 dz2hν

[V(H2O)6]3+

dxy dxz dyz

dx2-y2 dz2

3T1,2 3A23T1

Electronic Difference Densities

d-d Transition

Red = Electron Gain Yellow= Electron Loss

LMCT Transition MLCT Transition π→π* Transition

Spectroscopy and States

0SMΓ

I ′S ′M ′Γ

J ′′S ′′M ′′Γ

K ′′′S ′′′M ′′′Γ

Ener

gy

Apply some kind of oscillating perturbing field with Hamiltonian H1(ω) in order to induce transitions between different states of the system

Intensity

Transition Probability („Fermi‘s Golden Rule“)

I ∝ Ψ

initial| H

1| Ψ

final

2

Light Matter Interaction

H1= Z

A

!RA,a

A∑ −

!ri,a

i∑

H1= (

!ri,a

!ri,b− 13ri2δab)

i∑

H1= 12(!li+ 2!si)a

i∑

Electric Dipole

Magnetic Dipole

Electric Quadrupole

In atomic units for a randomly oriented sample

fED

=23(E

f−E

i) Ψ

i|!µ

ED,a| Ψ

f

2

a=x ,y,z∑

fMD

=23α2(E

f−E

i) Ψ

i|!µ

MD,a| Ψ

f

2

a=x ,y,z∑

fEQ

=120α2(E

f−E

i)3 Ψ

i|!µ

EQ,ab| Ψ

f

2

ab=x ,y,z∑

ABS, MCD

XAS

CD, EPR

Spectroscopic Selection Rules

Ψinitial| H

1|Ψ

final

2

★ The information about the allowedness of a transition is contained in:

★ Spin-Selection rule: ➡ The initial and final states must have the same total spin ➡ This is a strong selection rule up to the end of the first transition row. Beyond

this, strong spin-orbit coupling leads to deviations

★ Spatial-Selection rule: ➡ The direct product of Ψi, Ψf, and μ must contain the totally

symmetric irreducible representation ➡ This is a weak selection rule:something breaks the symmetry all the

time (environment, vibronic coupling, spin-orbit coupling, etc.)

Electric Dipole: Transforms as x,y,z If there is a center of inversion only g→u or u→g transitions are allowed, e.g. d-d transitions are said to be „Laporte forbidden“

Magnetic Dipole: Transforms as Rx,Ry, RzIf there is a center of inversion only g→g or u→u transitions are allowedElectric Quadrupole: Transforms as x2,y2,z2, xy,xz,yz

}

MCD Spectroscopy - How and Why?

LCPRCPLight SourceDetector

z

x

y

x

y

B-Field

The Magnetic Circular Dichroism Experiment

Monochromator Modulator

Sample

Liq. He Cryostat

Magnet

MCD = ALCP

B,T( )−ARCP

B,T( )− ALCP−A

RCP⎡⎣⎢

⎤⎦⎥B=0

Natural CD! "####### $#######

∝ cd Ef−E

i( ) Nj(B,T)

initialstates

∑ Ψj|%µ

ED,LCP| Ψ

f

2

− Ψj|%µ

ED,RCP| Ψ

f

2⎧⎨⎪⎪⎩⎪⎪

⎫⎬⎪⎪⎭⎪⎪final

states

∑

Does NOT Require a chiral substance!

Shielded Detector

Focussing Lens

Magneto Cryostat

B,T-Control

CD SpectrometerSample Cell

The MCD Instrument @ MPI/Mülheim

Why MCD Spectroscopy ?

‣ Sensitive Technique (esp. near-IR)‣ High Resolution (Signs)‣ Site Selective (Multiple Metal Sites)‣ Multidimensional (B,T,λ)‣ Does not require Isotopic Enrichment and is

not restricted to certain elements

‣ Has no Problems with Integer Spin ‣ Is not restricted to Para-

magnetic Species‣ Studies the Ground and

Excited States at the same

time‣ Puts Severe Constraints on

Possible Assignments

Dimensions of a MCD Experiment

λfix, Variable B,T

= Lineshape function

Stephens, P.J. (1976) Adv. Chem. Phys., 35, 197

ΔεE

= γβB −A1

∂f E( )∂E

+ B0

+C

0

kT

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟f E( )

⎧⎨⎪⎪⎪

⎩⎪⎪⎪

⎫⎬⎪⎪⎪

⎭⎪⎪⎪

Linear Limit:

Spectral Dimension Magnetic Dimension („VTVH MCD“)

General nonlinear MCD Theory: FN, EI Solomon (1998), Inorg. Chem., 38, 1847

MCD: Multidimensional Nature

[Fe(EDTA)(O2)]3-

Neese, F., Solomon, E.I. (1998) J. Am. Chem. Soc., 120, 12829

MCD: Resolution

Neese, F.; Zaleski, J.M.; Loeb, K.E.; Solomon, E.I. (2000) J. Am. Chem. Soc., 122, 11703-11724

MCD: Site Selectivity

CuAHa

Ha3-CuB

e-

O2

H2O

Cytochrome c Oxidase

Thomson, A.J. (1997) In: Andrews, D.L. (Ed.) Perspectives in Modern Chemical Spectroscopy, Springer, Berlin, p. 243

MCD Fingerprinting: Heme-Cofactors

Marker Bands NIR-LS Fe(III)

CT-Spectra Axial LigandsCheesman, M. R.; Greenwood, C.; Thomson, A. J. Adv. Inorg. Chem. (1991), 36, 201

MCD: Integer Spin Systems

0+/-1

B-Field

hν (EPR)S=1 Ground State

S=1 Exc. State

0+/-1

hν (MCD)

Dgs

Des

Solvent Spectra

Thomson, A.J.; Cheesman, M.R.; George, S.K. (1993) Meth. Enzymol., 226, 199

MCD Spectroscopy of HS Fe(II) Systems

5C

5C

4C

6C10,000 cm-1

10,000 cm-15,000 cm-1

7,000 cm-1

<5,000 cm-1

5,000 cm-1

5,000 10,000 15,000Wavenumber (cm-1)

eg

t2g

a1

e

e

a1e

b1

b2

t2

e

Solomon et al. (1995) Coord. Chem. Rev., 144, 369

Studying Enzyme Mechanisms

O2, 2e-, 2H+

Rieske-Dioxygenases

Active Site Geometry from d-d Spectra

Holoenzyme

Rieske only

Difference

-Substrate +Substrate

6000 8000 10000 12000 14000 14000Energy (cm-1)

6000 8000 10000 12000 14000 14000Energy (cm-1)

Δε (M

-1 c

m-1

T-1

)

Δε (M

-1 c

m-1

T-1

)

Solomon et al., (2000) Chem. Rev., 100, 235-349

Mechanistic Ideas from Ligand Field Studies

Solomon et al., (2000) Chem. Rev., 100, 235-349

Fe2+ Fe2+ Fe2+

Fe4+ Fe3+Fe4+Fe4+

COO--OOCCOO--OOC COO--OOC

OO

COO--OOC

(O O)2-

COO--OOC

-O O (H+)

COO--OOC

H H-O O-

2H+COO--OOC

H H

HO OH

2e- from reductase

products

or

+O2

MCD Intensities

Some General Trends

✓ MCD spectra that show about equal amount of positive and negative intensity are typically dominated by SOC between excited states

✓ MCD spectra that predominantly show one sign are typically dominated by SOC between the G.S. and the excited states (e.g. orbitally nearly degenerate systems)

✓ d-d excited states SOC effectively with each other and hence show relatively strong MCD. LMCT/MLCT states SOC more weakly and hence show weak MCD. ➡ The ratio of Absorption to MCD intensity

(=C/D ratio) is an effective means to determine the nature of the transition as d-d or CT

Neese, F.; Zaleski, J.M.; Loeb, K.E.; Solomon, E.I. (2000) J. Am. Chem. Soc., 122, 11703-11724

Low-Spin Fe3+

MCD C/D Ratios and d-d vs CT Assignments ★ MCD intensity is associated with Spin-Orbit Coupling (SOC) ★ MCD (C-term) intensities are larger for d-d than for LMCT/MLCT transitions. ★ LMCT/MLCT transitions are usually much more intense in absorption. ➡ The ratio of Absorption to MCD intensity is a diagnostic of a d-d vs CT transition:

CD

=kTβB

ΔεMCD

(ν)

νdν∫

εABS

(ν)

νdν∫

Area under MCD band

Area under Absorption band

εABS > 5000-10000 AND C/D<0.01 → CT transition

εABS < 5000-10000 AND C/D>0.01 → d-d transition

MCD Example: CuCl42-

LMCT d-d

C/D~0.02

C/D~0.002

dz2→dx2-y2 dxz,yz→dx2-y2

dxy→dx2-y2

Established signs for CuII-MCD: dxz,yz→dx2-y2 : (+,-) ,pseudo-A‘ dxy→dx2-y2 : (-) dz2→dx2-y2 : (+)

Theory of MCD Spectroscopy

MCD Versus Ground State Methods

Electronic Ground State

Multiplet

Electronically Excited State

Multiplet

Total Spin S

2S+1 ComponentsMS=S,S-1,...,-S

Total Spin S‘

2S‘+1 ComponentsM‘S=S‘,S‘-1,...,-S‘

ΔE~5,000-45000 cm-1

ΔE~0-10 cm-1

ΔE~0-10 cm-1

∝ Ground State SH: ggs,Dgs,Jgs,...

∝ Excited State SH: ges,Des,Jes,...

Electronic Transitions

Probed with MCD

EPR Transition

21−

21−

21+

21+

Magnetic Field

Bg gsβ

Bgesβ

Dimensions of a MCD Experiment

λfix, Variable B,T

= Lineshape function


ΔεE

= γβB −A1

∂f E( )∂E

+ B0

+C

0

kT

⎛

⎝

⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟f E( )

⎧⎨⎪⎪⎪

⎩⎪⎪⎪

⎫⎬⎪⎪⎪

⎭⎪⎪⎪

Linear Limit:

Spectral Dimension Magnetic Dimension („VTVH MCD“)

General nonlinear MCD Theory: FN, EI Solomon (1998), Inorg. Chem., 38, 1847

Angular Momentum

Photons:

Cohen-Tanudji, C. et al. (1977) Quantum Mechanics, John-Wiley & Sons

Energy:

Momentum:

Angular Momentum:

• The Total Angular Momentum (Electrons and Photons) is Conserved• A Linearly Polarized Light Beam Contains Photons in a Superposition State• A Circularly Polarized Light Beam Contains Photons in a Pure Angular Momentum State

Craig, DP; Thrunamachandran, T (1984) Molecular Quantum Electrondynamics, Dover Publications

Electrons:Energy:

Momentum:

Angular Momentum: spin

orbit

MCD A-Terms: A 1S 1P Transition

1S

1P

1S0

1P0

1P-1

1P1

rcp lcpm+1 m-1


MCD C-Terms: A 1P 1S Transition1S

1P

1S0

1P0

1P-1

1P1

rcplcpm+1m-1


MCD B-Terms:From Perturbation Theory:

Ø Mixing of the excited state or the ground State to potentially all other states via

the Zeeman interactionØ Inversely proportional to ΔE

Ø Absorption Shaped and Temperature IndependentØ Physically Intuitive Picture ?Ø Dominates MCD of Organic Molecules with Nondegerate Singlet Ground States


For the Model 1P to 1S Transition

Insert:

Assume: FWHM=

A-term:

C-term:

Ratio A:B:C

Relative Magnitude of A- B- and C-Terms

A:B:C ≈ 1 : 0.1 : 5


rcplcp

Boltzmann Population

Population Difference

Variable Temperature Variable H-Field MCDStephens, P.J. (1976) Adv. Chem. Phys., 35, 197

Magnetization Curves of S=1/2 Systems

VTVH MCD for S>1/2 Systems

T

Observations: • The MCD Signal Varies Nonlinearly with B and T • The Curves Recorded at Different Temperatures do not Overlay (=Nesting) • The Signal may Pass Through a Maximum and then Decrease Again or may even Change Sign

Behavior was not Understood

A New Theory was Needed

Assumptions + Perturbation Theory (Hso, Hze)

Spin Hamiltonian!!FN; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

General Ansatz:

(Lengthy Derivation)

Summary: A general theory of MCD

General Theory for Nonlinear MCD

Neese, F.; Solomon, E.I. (1999) Inorg. Chem., 38, 1847

Direction Cosines (Orientation of B in the Molecular Frame)

Expectation Value of Sx,y,z for the SH Eigenstate i

Boltzmann Population of SH Eigenstate i

Orthogonal Effective Product of Transition Dipole Moments

Collection of ConstantsExperiment

Spin-Hamiltonian

(ALL B,T dependence)

Nature of Ground and

Excited States

Parameterization in terms of Spin-Hamiltonian and State Specific Polarization Parameters Achieved for the First Time

Experimental Test: Fe(TPP)Cl (S=5/2)

Experimental Data: Browett, WR; Fucaloro, AF; Morgan, TV; Stephens, PJ J. Am. Chem. Soc., 105

Theoretical Prediction: 4D

2D

6S

S=5/2

Sum

Exp.

Theo.


Check the theory

The effective g-value perpendicular to the plane of polarization

determines the amount of nesting

4D

2D

6S

(The Effective g-values are read from the rhombogram)


MCD and ZFS: Weak field case

The MCD magnetization for vanishing ZFS behaves exactly like a Brillouin

Function for spin S

Attention: May be Difficult to Distinguish from Case with large ZFS and Easy Axis

Polarization

Uncritically Assumed in (too) Many Studies!


MCD and ZFS: Strong field case

Intermediate Field Case

Transition Polarizations

Electronic Transitions have a Direction

xy

z

E-Vector Orientation

x

yz

[Cu1.5...Cu1.5(SCys)2(NHis)4]+

The MCD Equations knows something about it!

ΔεE=γ4πS

NilxMyzeff S

x i+ l

yMxzeff S

y i+ l

zMxyeff S

z i

⎡

⎣⎢⎢

⎤

⎦⎥⎥i

∑ sin θdθdφ∫∫

effective transition dipole productMxyeff (one direction is intrinsically allowed and an

orthogonal direction has to come from spin-orbit coupling with an orthogonally polarized excited

state)

If you have fitted the three products for a given band, you can figure out the linear polarization:

%mx= 100x

(MxyeffM

xzeff )2

(MxyMxz)2 + (M

xyMyz)2 + (M

xzMyz)2

Transition Polarizations from Randomly Oriented Samples


z-pola rized

yz-pola rized

xz-pola rized

Transition Assignments from MCD


Insights into Metal-Ligand Bonding


✓ MCD measures the differential absorption of left- and right circularly polarized light as a function of:

- Wavelength

- Magnetic Field

- Temperature

‣ MCD exists in all matter, does not require isotopes, paramagnetism, half-integer spin … ‣ MCD can be applied over the whole spectral range (200-2000 nm) ‣ MCD provides powerful fingerprints (even if you understand nothing what it means!) ‣ MCD can be site selective in systems with multiple sites ‣ MCD - unlike SQUID - is NOT a bulk measurement and hence impurity insensitive ‣ MCD as a function of B,T can be viewed as an optical measurement of magnetism

‣ MCD as a function of B,T and l provides transition polarization information in solution

‣ MCD to ABS ratios provide information about d-d vs charge transfer transitions ‣ MCD signs are powerful probes of the nature of electronic transitions ➡ MCD is an extremely powerful link between electronic ground state (EPR) and excited

states (ABS) methods

Summary and Conclusions

★ MCD is a powerful and versatile spectroscopic technique for investigating open shell species.

★ It roughly contains the information of (polarized) absorption spectroscopy and magnetic susceptibility in a site selective fashion.

★ The theory of the nonlinear MCD behavior is now understood and widely used.

★ The quantum chemical calculation of MCD spectra of larger molecules very challenging as multireference, dynamic correlation, spin dependent relativistic effects and magnetic field perturbations must be considered simultaneously.

★ A particularly challenging case is met for magnetically interacting transition metal ions for which MCD golds great promise.

Have fun with .... ORCA

http://www.thch.uni-bonn.de/tc/orca

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